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Over the years, the recommender systems (RS) have witnessed an increasing growth for its enormous benefits in supporting users’ needs through mapping the available products to users based on their observed interests towards items. In this setting, however, more users, items and rating data are being constantly added to the system, causing several shifts in the underlying relationship between users and items to be recommended, a problem known as concept drift or sometimes called temporal dynamics in RS. Although the traditional techniques of RS have attained significant success in providing recommendations, they are insufficient in providing accurate recommendations due to concept drift problems. These issues have triggered a lot of researches on the development of dynamic recommender systems (DRSs) which is focused on the design of temporal models that will account for concept drifts and ensure more accurate recommendations. However, in spite of the several research efforts on the DRSs, only a few secondary studies were carried out in this field. Therefore, this study aims to provide a systematic literature review (SLR) of the DRSs models that can guide researchers and practitioners to better understand the issues and challenges in the field. To achieve the aim of this study, 87 papers were selected for the review out of 875 total papers retrieved between 2010 and 2019, after carefully applying the inclusion/exclusion and the quality assessment criteria. The results of the study show that concept drift is mostly applied in the multimedia domain, then followed by the e-commerce domain. Also, the results showed that time-dependent neighborhood models are the popularly used temporal models for DRS followed by the Time-dependent Matrix Factorization (TMF) and time-aware factors models, specifically Tensor models, respectively. In terms of evaluation strategy, offline metrics such as precision and recalls are the most commonly used approaches to evaluate the performance of DRS.